Unit 4.4 Skills Check: Fundamental Theorem of Algebra

What is the Degree of this polynomial:
f(x)= x³(x + 3)²(x – 5)

• Degree: 6
• Degree: 5
• Degree: 3
• Degree: 2

The degree of the polynomial determines the number of roots.

• True
• False

The Fundamental Theorem of Algebra tell us two things. Which of the options does not come from the Fundamental Theorem of Algebra?

• A nth degree polynomial has at least 1 complex solution

• An nth degree polynomial always has 2 x-intercepts

• A nth degree polynomial has n solutions (roots).

Which statement is the Fundamental Theorem of Algebra?

• There are infinitely many rationals between two reals.

• Every polynomial equation having complex coefficents and degree greater than the number 1 has at least one complex root.

• There are infinitely many prime numbers.

• All numbers are rational numbers.

A Polynomial of Degree 6 CAN have the following number of imaginary roots:

• 1
• 4
• 3
• 8

What is the least degree of the following polynomial that has 4 real roots and 2 imaginary roots?

• 4

• 2

• 8

• 6

What is the least degree of a polynomial that contains the roots of -2 and 4i ?

• 3

• 4

• 1

• 2

If 2i is a zero, then

• 2i repeats twice
• -2i is a zero too
• 1-2i is a zero too
• 0+2i is a zero too

If 2+3i is a zero of a polynomial function what must another zero be?

• 2-3i

• 2+3i

• -2-3i

• -2+3i

All imaginary roots come in pairs.

• True

• False